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When you have mastered numbers, you will in fact no longer be reading numbers, any more than you read words when reading books. You will be reading meanings.
Do you know what the mathematical expression is for longing? ... The negative numbers. The formalization of the feeling that you are missing something.
A mathematician is a magician who converts adjectives into nouns: continuous into continuum, infinite into infinity, infinitesimal into location, 0D into point, 1D into line, curved into geodesic...
A mathematician is an individual who constructs space with 0D particles and then places a bowling ball on this invisible canvas to explain how gravity works.
Only three constants are significant for star formation: the gravitational constant, the fine structure constant, and a constant that governs nuclear reaction rates.
Surely, the gods' judgment is certain. But as for us, we must be satisfied to 'come close' to those things, for we are men, who speak according to what is likely, and whose lectures resemble fables.
There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else — but persistent.
A mathematician tells you that the wall of warped space prevents the Moon from flying out of its orbit yet can't tell you why an astronaut can go back and forth across that same space.
...317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is, because mathematical reality is built that way.
...no thought, if it be non-mathematical in spirit, can be trusted, and, although mathematicians sometimes make mistakes, the spirit of mathematics is always right and always sound.
Overstimulation has been the real drawback. I need to find ways to stop thinking about analysis of algorithms, in order to do various other things that human beings ought to do.
The best mathematics is serious as well as beautiful—‘important’ if you like, but the word is very ambiguous, and ‘serious’ expresses what I mean much better
REAL MATHEMATICS is not about just computing but it is about figuring out…Figuring out the truthfulness, reasoning behind specific event, patterns, determinism in chaotic processes etc.
The play is independent of the pages on which it is printed, and ‘pure geometries’ are independent of lecture rooms, or of any other detail of the physical world.